A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem

TL;DR

This paper introduces a novel Monte Carlo algorithm for Gaussian process classification that simplifies computation, improves reliability, and increases speed over existing methods by transforming the problem into evaluating Gaussian orthant integrals.

Contribution

It develops a new derivation and Monte Carlo procedure for Gaussian process classification, transforming the problem into Gaussian orthant integrals and enhancing computational efficiency.

Findings

The new method is simpler and more reliable than MCMC.

It offers faster computation for Gaussian process classification.

The approach effectively evaluates intractable integrals in classification.

Abstract

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.